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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 774 · 40 questions
TalentJR

How to solve it (Think in totals): Average = total ÷ how many; so total = average × how many. A number taken away = old total − new total. Evenly spaced numbers (like 10 to 20): average = (first + last) ÷ 2.

NameDateTime takenScore ___ / 40
  1. 1.The average of 8 numbers is 18. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 40 (b) 18 (c) 31 (d) 53
  2. 2.A batter has an average of 42 runs in 3 matches. How many runs are needed in the next match to raise the average to 45? (a) 12 (b) 45 (c) 48 (d) 54
  3. 3.What is the average of 16, 30, 10, 17, 35 and 42? (a) 24 (b) 25 (c) 26 (d) 30
  4. 4.What is the average of all the whole numbers from 33 to 69? (a) 36 (b) 18 (c) 52 (d) 51
  5. 5.The average of 8 numbers is 29. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 8 (b) 9 (c) 61 (d) 29
  6. 6.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 41 (b) 86 (c) 13 (d) 14
  7. 7.A batter has an average of 51 runs in 8 matches. How many runs are needed in the next match to raise the average to 54? (a) 54 (b) 78 (c) 27 (d) 57
  8. 8.A batter has an average of 26 runs in 7 matches. How many runs are needed in the next match to raise the average to 29? (a) 29 (b) 24 (c) 50 (d) 32
  9. 9.The average of 5 numbers is 39. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 19 (b) 20 (c) 83 (d) 39
  10. 10.What is the average of all the whole numbers from 18 to 58? (a) 40 (b) 39 (c) 38 (d) 20
  11. 11.What is the average of all the whole numbers from 16 to 42? (a) 29 (b) 26 (c) 13 (d) 30
  12. 12.What is the average of all the whole numbers from 41 to 81? (a) 62 (b) 61 (c) 20 (d) 40
  13. 13.What is the average of 77, 65, 95, 66, 68 and 109? (a) 96 (b) 79 (c) 81 (d) 80
  14. 14.A batter has an average of 41 runs in 3 matches. How many runs are needed in the next match to raise the average to 47? (a) 47 (b) 65 (c) 24 (d) 53
  15. 15.What is the average of all the whole numbers from 14 to 22? (a) 19 (b) 18 (c) 8 (d) 4
  16. 16.The average of 4 numbers is 49. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 49 (b) 40 (c) 41 (d) 101
  17. 17.What is the average of 83, 75, 69, 79 and 79? (a) 79 (b) 76 (c) 78 (d) 77
  18. 18.What is the average of all the whole numbers from 12 to 42? (a) 15 (b) 28 (c) 30 (d) 27
  19. 19.A batter has an average of 57 runs in 8 matches. How many runs are needed in the next match to raise the average to 65? (a) 65 (b) 72 (c) 73 (d) 129
  20. 20.What is the average of 11, 36, 19, 22 and 37? (a) 27 (b) 25 (c) 26 (d) 24
  21. 21.A batter has an average of 25 runs in 9 matches. How many runs are needed in the next match to raise the average to 30? (a) 75 (b) 50 (c) 35 (d) 30
  22. 22.A batter has an average of 21 runs in 3 matches. How many runs are needed in the next match to raise the average to 29? (a) 32 (b) 29 (c) 53 (d) 37
  23. 23.The average of 5 numbers is 33. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 22 (b) 69 (c) 21 (d) 33
  24. 24.What is the average of all the whole numbers from 46 to 54? (a) 51 (b) 50 (c) 8 (d) 4
  25. 25.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 6 (b) 40 (c) 69 (d) 35
  26. 26.What is the average of all the whole numbers from 43 to 55? (a) 50 (b) 49 (c) 12 (d) 6
  27. 27.A batter has an average of 54 runs in 6 matches. How many runs are needed in the next match to raise the average to 56? (a) 56 (b) 68 (c) 58 (d) 14
  28. 28.What is the average of all the whole numbers from 58 to 66? (a) 4 (b) 62 (c) 63 (d) 8
  29. 29.A batter has an average of 57 runs in 6 matches. How many runs are needed in the next match to raise the average to 59? (a) 14 (b) 59 (c) 61 (d) 71
  30. 30.What is the average of 71, 66, 43, 68 and 42? (a) 59 (b) 60 (c) 57 (d) 58
  31. 31.What is the average of 8, 11, 8, 13 and 65? (a) 20 (b) 21 (c) 23 (d) 22
  32. 32.A batter has an average of 58 runs in 9 matches. How many runs are needed in the next match to raise the average to 66? (a) 74 (b) 138 (c) 66 (d) 80
  33. 33.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 43 (b) 93 (c) 46 (d) 42
  34. 34.What is the average of 66, 72, 72, 74, 62 and 92? (a) 75 (b) 73 (c) 72 (d) 74
  35. 35.A batter has an average of 39 runs in 9 matches. How many runs are needed in the next match to raise the average to 47? (a) 80 (b) 47 (c) 55 (d) 119
  36. 36.What is the average of 31, 51, 40, 49 and 14? (a) 38 (b) 36 (c) 39 (d) 37
  37. 37.The average of 5 numbers is 33. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 25 (b) 53 (c) 61 (d) 33
  38. 38.The average of 5 numbers is 12. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 26 (b) 12 (c) 5 (d) 4
  39. 39.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 36 (b) 5 (c) 71 (d) 40
  40. 40.What is the average of 59, 76, 59, 54, 74 and 74? (a) 65 (b) 66 (c) 67 (d) 68

Answer key

  1. 53
  2. 54
  3. 25
  4. 51
  5. 8
  6. 13
  7. 78
  8. 50
  9. 19
  10. 38
  11. 29
  12. 61
  13. 80
  14. 65
  15. 18
  16. 40
  17. 77
  18. 27
  19. 129
  20. 25
  21. 75
  22. 53
  23. 21
  24. 50
  25. 40
  26. 49
  27. 68
  28. 62
  29. 71
  30. 58
  31. 21
  32. 138
  33. 42
  34. 73
  35. 119
  36. 37
  37. 53
  38. 4
  39. 40
  40. 66

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